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SPECIAL VALUES OF SHIFTED CONVOLUTION DIRICHLET SERIES

Published online by Cambridge University Press:  16 June 2015

Michael H. Mertens
Affiliation:
Mathematisches Institut der Universität zu Köln, Weyertal 86–90, D-50931 Köln, Germany email mmertens@math.uni-koeln.de
Ken Ono
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30022, U.S.A. email ono@mathcs.emory.edu
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Abstract

In a recent important paper, Hoffstein and Hulse [Multiple Dirichlet series and shifted convolutions, arXiv:1110.4868v2] generalized the notion of Rankin–Selberg convolution $L$-functions by defining shifted convolution$L$-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.

Type
Research Article
Copyright
Copyright © University College London 2015 

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